At the time of his birth Grothendieck's mother was married to Johannes Raddatz, a German journalist, and his birthname was initially recorded as Alexander Raddatz.

However, most modern algebraic geometry texts starting with Alexander Grothendieck's foundational EGA use the convention in this article .< ref > A notable exception to modern algebraic geometry texts following the conventions of this article is Commutative algebra with a view toward algebraic geometry / David Eisenbud ( 1995 ), which uses " h < sub > A </ sub >" to mean the covariant hom-functor.

Fundamental groups also appear in algebraic geometry and are the main topic of Alexander Grothendieck's first Séminaire de géométrie algébrique ( SGA1 ).

Earlier in his career Mackey did significant work in the duality theory of locally convex spaces, which provided tools for subsequent work in this area, including Alexander Grothendieck's work on topological tensor products.

Alexander Grothendieck's version of the Riemann – Roch theorem was originally conveyed in a letter to Jean-Pierre Serre around 1956 – 7.

It is likely that the work was not written by Alexander himself, but rather by his pupils on the basis of debates involving Alexander.

He was a favorite of Alexander the Great, whom he accompanied in his Persian campaigns, and wrote a third historical work on Alexander.

Alexander believed his work could be applied to improve individual health and well being.

Sir Stafford Cripps, George Bernard Shaw, Henry Irving and other stage grandees, Lord Lytton and other eminent people of the era also wrote positive appreciations of his work after taking lessons with Alexander.

Fritz Perls, who originated Gestalt therapy, credited Alexander as an inspiration for his psychological work .< ref >

In 1924 in the UK the chemist Harold Plenderleith began to work at the British Museum with Dr. Alexander Scott in the newly created Department of Scientific and Industrial Research, thus giving birth to the conservation profession in the UK.

' Euan MacKie would place the origin even later, stating: "... the genesis and modern flowering of archaeoastronomy must surely lie in the work of Alexander Thom in Britain between the 1930s and the 1970s.

In the 1960s the work of the engineer Alexander Thom and that of the astronomer Gerald Hawkins, who proposed that Stonehenge was a Neolithic computer, inspired new interest in the astronomical features of ancient sites.

The claims of Hawkins were largely dismissed, but this was not the case for Alexander Thom's work, whose survey results of megalithic sites hypothesized widespread practice of accurate astronomy in the British Isles.

Authorship is more contentious for this work ; although he started this work, he died before it could be finished, and most likely was more a product of people other than Alexander.

Daniel Kehlmann's 2005 novel Die Vermessung der Welt, translated into English as Measuring the World ( 2006 ), explores Gauss's life and work through a lens of historical fiction, contrasting them with those of the German explorer Alexander von Humboldt.

It shows the influence of Walter Scott, and Brontë's modifications to her earlier gothic style have led Christine Alexander to comment that, in the work, " it is clear that Brontë was becoming tired of the gothic mode per se ".

Alexander is often overlooked by texts in the history and theory of architecture because his work intentionally disregards contemporary architectural discourse.

Dia was originally created by Alexander Larsson but he moved on to work on GNOME and other projects.

The FIDE Congress in Vienna in 1957 adopted new regulations, called the FAV system, in recognition of the work done by International Judge Giovanni Ferrantes ( Italy ), Alexander ( probably Conel Hugh O ' Donel Alexander ), and Giancarlo Dal Verme ( Italy ).

The other authors from the romanticism era include: Antony Pogorelsky ( penname of Alexey Alexeyevich Perovsky ), Orest Somov, Alexandr Pushkin, Nikolai Alekseevich Polevoy, Mikhail Lermontov ( his work Stuss ) and Alexander Bestuzhev-Marlinsky.

Critic Alexander Woollcott wrote of Bogart's early work that he " is what is usually and mercifully described as inadequate.

Bradley, now the American commander of the 12th Army Group, remarked that he would have preferred to work with Alexander, rather than Montgomery, as he regarded the former as " a restrained, self-effacive, and punctilious soldier ".

Alexander Luria's earlier work on neuropsychological processes lead to the PASS theory ( 1997 ).

He, Alexander Hamilton and John Jay wrote the Federalist Papers, a series of 85 newspaper articles published in New York to explain how the proposed Constitution would work, mainly by responding to criticisms from anti-federalists.

During this sequence, it is revealed that Mrs. Alexander died from the injuries inflicted during the gang-rape, and her husband has decided to continue living " where her fragrant memory persists " despite the horrid memories.

Thebe, Alexander's wife and cousin ( or half-sister, as the daughter of Jason of Pherae ), concealed her three brothers in the house during the day, had the dog removed when Alexander had gone to rest, and, having covered the steps of the ladder with wool, brought up the young men to her husband's chamber.

In 1931, during the refurbishment of Vilnius Cathedral, the forgotten sarcophagus of Alexander was discovered, and has since been put on display.

Though he was destined to be a strongly counter-reforming emperor, Alexander had little prospect of succeeding to the throne during the first two decades of his life, as he had an elder brother, Nicolas, who seemed of robust constitution.

Plutarch tells a story that at Bactra, in 327 BC in a debate with Callisthenes, he advised all to worship Alexander as a god even during his lifetime, is with greater probability attributed to the Sicilian Cleon.

However, during the schism between Pope Alexander III and Antipope Victor IV, Absalon stayed loyal to Valdemar even as he joined the Holy Roman Emperor Frederick Barberossa in supporting Victor IV.

The technique is named after actor Frederick Matthias Alexander, who developed its principles in the 1890s as a personal tool to alleviate breathing problems and hoarseness during public speaking.

Alexander was a Shakespearean orator who developed voice loss during his performances.

Teacher training was interrupted during World War II between 1941 and 1943, when Alexander accompanied children and teachers of the Little School to Stow, Massachusetts to join his brother.

The American philosopher and educator John Dewey became impressed with the Alexander technique after his headaches, neck pains, blurred vision, and stress symptoms largely improved during the time he used Alexander's advice to change his posture.

Alexander Fyodorovich Kerensky (, ; – 11 June 1970 ) was a major political leader before and during the Russian Revolutions of 1917.

Two convicts, Henry and Susannah Kable, sought to sue Duncan Sinclair, the captain of Alexander, for stealing their possessions during the voyage.

The basic methods were developed by Alexander Thom during his extensive surveys of British megalithic sites.

* Sally Hobart Alexander became blind when she was about 25 and a schoolteacher, during the 1970s, because of an eye disease.

These hardy tribes had offered stubborn resistance to Alexander ( 326 c BC ) during latter's campaign of the Kabul, Kunar and Swat valleys and had even extracted the praise of the Alexander's historians.

Alexander the Great introduced the idea of using them to provide cover on the battlefield in addition to using them during sieges.

Some companies, particularly breweries such as Alexander Keith's and Moosehead have played up a connection between folklore with alcohol consumption during their marketing campaigns.

Apart from his lengthy teaching career at Berkeley ( during which a number of international students began to appreciate and apply his methods ), Alexander was a key member of faculty both of The Prince of Wales's Summer Schools in Civil Architecture ( 1990 – 1994 ) and The Prince of Wales's Institute of Architecture

Alexander Graydon, with whom Allen was paroled during his captivity in New York, described him like this:

Despite the arguably greater architectural inventiveness of Borromini and Cortona, Bernini's artistic pre-eminence, particularly during the reigns of popes Urban VIII ( 1623 – 1644 ) and Alexander VII ( 1655 – 1665 ), meant he was able to secure the most important commission in the Rome of his day, St. Peter's Basilica.

" Although he did not fare so well during the reign of Innocent X, under Alexander VII, he once again regained pre-eminent artistic domination and continued to be held in high regard by Clement IX.

Further observations were made by the German explorer Alexander von Humboldt during his South American journey from 1799 to 1803.

Alexander the Great and his Macedonian army arrived to what is now Afghanistan in 330 BC after conquering Persia during the Battle of Gaugamela.

Alexander, between 23 and 30 March 1918, had to assume command of the 4th Guards Brigade, during the British retreat.